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Proof about operations on sets

  1. Mar 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Let the set Ar: r is an element of all real numbers and the set Br: r is an element of all real numbers be two indexed families of sets.

    Prove that (upside U r is an element of the reals Ar) U (upside U r is an element of the reals Br) is a subset of upside U r is an element of the reals (ArUBr).


    2. Relevant equations



    3. The attempt at a solution

    Could someone please give me a hint? I know that Ar and Br have to be unions of each other and at the same they are subsets of the other one, but I don't really know how I would go about proving this.

    Thank you much
     
  2. jcsd
  3. Mar 9, 2008 #2

    Dick

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    Homework Helper

    That's kind of hard to read. But if x is an element of the left hand side, then it's either in all of the A_r or it's in all of the B_r. If x is in the right hand side then it's in either A_r or B_r for all r. Assume each of the conditions on the left and prove they imply the right.
     
  4. Mar 9, 2008 #3
    Thank you very much

    Regards
     
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